MAI0115
Optimal control, brief introductory course

Number of credits: 1 hp

Examiner: Gunnar Aronsson

Course literature: J. Macki, A. Strauss: Introduction to optimal control theory, Springer Verlag 1995. Lawrence C. Evans: An introduction to mathematical optimal control theory; Version 0.2. University of California, Berkeley. Lecture notes, available from Evans' home page.

Course contents:

1. Some mathematical basics, like: Caratheodory solution concept for ODE; Mayer problem, Bolza problem; Big-bang principle (without proof); variational system, adjoint system; Time-optimal problems; "Spike variations".
2. First cases of a Boltyanski-Pontryagin maximum principle; Adjoint response, transversality condition; Adjoint vector seen as shadow values; Hamiltonian function; Economic interpretation of the maximum principle; Hamilton-Jacobi-Bellman equation.
3. Examples, most of them from economics.
4. Deriving a maximum principle for problems with fixed time and fixed end-point. A more difficult Bolza problem. Basic perturbation formula. A covering property of continuous mappings; A B-P maximum principle.

Organisation: 10 teorilektioner + 4 lektioner för lösning av övningsuppgifter.

Examination: Tillräcklig närvaro under kursen + deltagande i problemlösning.

Prerequisites: Flevariabelanalys + (helst) någon kunskap om ordinära differentialekvationer.

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Last updated: 2022-11-15